 Research
 Open Access
 Published:
Detecting complexes from edgeweighted PPI networks via genes expression analysis
BMC Systems Biology volume 12, Article number: 40 (2018)
Abstract
Background
Identifying complexes from PPI networks has become a key problem to elucidate protein functions and identify signal and biological processes in a cell. Proteins binding as complexes are important roles of life activity. Accurate determination of complexes in PPI networks is crucial for understanding principles of cellular organization.
Results
We propose a novel method to identify complexes on PPI networks, based on different coexpression information. First, we use Markov Cluster Algorithm with an edgeweighting scheme to calculate complexes on PPI networks. Then, we propose some significant features, such as graph information and gene expression analysis, to filter and modify complexes predicted by Markov Cluster Algorithm. To evaluate our method, we test on two experimental yeast PPI networks.
Conclusions
On DIP network, our method has Precision and FMeasure values of 0.6004 and 0.5528. On MIPS network, our method has FMeasure and S_{ n } values of 0.3774 and 0.3453. Comparing to existing methods, our method improves Precision value by at least 0.1752, FMeasure value by at least 0.0448, S_{ n } value by at least 0.0771. Experiments show that our method achieves better results than some stateoftheart methods for identifying complexes on PPI networks, with the prediction quality improved in terms of evaluation criteria.
Background
Detecting of protein complexes from PPI networks is a key problem to elucidate protein functions and identify biochemical, signal and biological processes in a cell. Like other biological molecules, most proteins do not work in isolation; they cooperate with other proteins to perform a particular biological function. These complexes are molecular aggregations of two or more proteins assembled by PPIs [1]. Accurate determination of complexes in PPI networks is crucial for understanding principles of cellular organization.
In past several years, a large number of technologies have been developed for the largescale analysis of complex detection from PPI networks [2–13]. Heuristicbased algorithms find dense network regions by searching heuristically for potential cluster regions using an iterative greedy seed and extend strategy, one of the seminal efforts is MCODE [14] and proposed a densitybased clustering approach to detect complexes, which picked vertices with large weights as initial clusters and further augmented them to detect dense connective clusters. Similar to MCODE, AltafUIAmin proposed an algorithm called DPClus [15] with good accuracy. Li [16] proposed IPCA, it searches for subgraphs having small diameter and whose cluster property is above the interaction probability threshold. And RestrictedNeighborhoodSearch Clustering (RNSC) algorithm [17] deploys a costbased partitioning algorithm. The ClusterONE method [18], detects overlapping clusters in a PPI network using a greedy seed and extend heuristic, an advantage of ClusterONE is the ability to not just find overlapping clusters, but also clusters that may be contained in another cluster.
One of the most widely used graph clustering algorithm is Markov Cluster Algorithm (MCL) [19], which is a fast and robust method, which simulate random walk in the graph to cluster. Lots of studies indicated that MCL can tolerate more noises than other clustring algorithms on PPI networks [8]. Algorithms such as RMCL [20], SRMCL [21], MCLCA [22] and RRW [23] were proposed to overcome further weaknesses of MCL. However, SRMCL still predicted too many complexes, and RRW predicted complexes of a particular size. On the basis of these limitations, we design a novel edgeweighting MCL method to detect complexes on PPI networks, which can effectively improve accuracy of clustering results. Then, there are some classic clustering algorithms that can be used on the ClustEval framework [24], such as DBSCAN [25], Spectral Clustering [26], Transitivity Clustering [27], fanny [28], but our study is not a complete clustering problem, classical clustering algorithm need combining with the postprocessing or some improvements.
Complete enumeration algorithms aim to enumerate all possible subgraphs in G with density exceeding a specified threshold. Spirin and Mirny [29] proposed three techniques for detecting protein complexes and functional modules from PPI networks. The first approach finds cliques as modules by complete enumeration. The second approach leverages the notion of superparamagnetic clustering (SPC), which assigns to each vertex a spin with several states. Lastly, they proposed a Monte Carlo optimizationbased technique (MC) where finding highly connected set of vertices is formulated as an optimization problem. The CFinder method [30] identifies a set of kclique modules in a PPI network where kcliques correspond to k node complete subgraphs of G with a maximum density of 1. It is based on a deterministic approach called the Clique Percolation Method (CPM) [31], which generates overlapping clusters by finding kclique percolation communities. Then, Cui [32] showed on the yeast PPI network that nearcliques may reveal better quality functional modules compared to overlapping cliques. The Clustering−basedonMaximal Cliques (CMC) [33] method generated maximal cliques from a weighted PPI network and combined or removed them, considering to connectivity and overlapping rate. A common theme among complete enumeration algorithms is exhaustive search. While such search enables identification of all relevant modules within a PPI network, it is computationally expensive. Therefore, their applications are limited to relatively small PPI networks.
Leung [34] developed a coreattachment approach for identifying complexes from PPI networks of single species and studying the organization of complexes. Ulitsky and Shamir [10] reformulated the problem of finding modules with high confidence connectivity as finding subgraphs to satisfy a weight threshold of their minimum cut. Shi [11] proposed a neural networkbased semisupervised learning method, which leverages proteomic features of subgraphs in a weighted PPI network with their topological features to generate complexes. Macropol [23] proposed a protein complex prediction algorithm, named by RRW, which constructed a cluster of proteins according to the stationary probability of a random walk. Maruyama [35] extended the RRW by introducing a random walk via restarts with a cluster of proteins, each of which is weighted by the sum of strengths for directly physical interactions. Also, Maruyama proposed a novel method based on random walks, Naive Bayes classifiers, and sampling methods [36–40].
Above methods only focus on static PPI networks. In reality, PPI networks in a cell are not static but dynamic [41–43]. The dynamic PPI network can be changing over time, environments and different stages of cell cycles [44, 45]. Lots of methods used dynamic PPI networks to predict complexes accurately [46, 47]. Li [12] proposed a new DPC algorithm to identify complexes based on gene expression profiles and PPI networks, based on static expressed core in all molecular cycles and shortlived dynamic attachments. Also, Luo [13] proposed a DCA method to identify more accurate protein complexes in dynamic PPI networks. Srihari [48] incorporated time in the form of cellcycle phases into the analysis of complexes from PPI networks and studied the temporal phenomena of complex assembly and disassembly across phases.
Existing methods constructed PPI networks, based on gene expression variance of each protein [49, 50]. Segal [7] introduced a unified probabilistic model to detect functional modules from gene expression, based on the assumption that genes in the same pathway display similar expression profiles and products of genes work together to accomplish certain task. Maraziotis [9] proposed a DMSP algorithm finding functional modules by integrating gene expression and PPI data. In general, if a protein is at active time point, the expression level of corresponding gene is at the peak point. Some researchers use the dynamic information from gene expression data to construct timeevolving dynamic protein interaction networks, which divided proteins into active and inactive and combined active proteins at the same time to form a new network [12, 31, 42, 43, 49, 50]. We design a new coexpression analysis method to measure each protein complex, based on differential coexpression information. Different proteins in the same complex have similar trend on gene expression intervals.
We propose a novel method to identify complexes on PPI networks. First, we design an edgeweighting MCL method to calculate complexes on PPI networks. Second, we propose a novel coexpression analysis method to evaluate predicted complexes, based on differential coexpression information. To evaluate our method, we test on two experimental yeast PPI networks. On DIP network, our method has Precision and FMeasure values of 0.6004 and 0.5528. On MIPS network, our method has FMeasure values of 0.3774. Comparing to existing methods, our method improves Precision value by at least 0.1752, FMeasure value by at least 0.0448, S_{ n } value by at least 0.0771.
Methods
We propose a novel method to identify protein complexes on PPI networks. First, we use Markov Cluster Algorithm with an edgeweighting scheme to calculate complexes on PPI networks. Second, we design a novel coexpression analysis method to measure each protein complex, based on differential coexpression information. Figure 1 shows the overall process of our method and the analysis pipeline to detect complexes from PPI network.
Edgeweighting scheme
A PPI network is formulated as an undirected graph G=(V,E), where v_{ i }∈V represents a protein and (v_{ i },v_{ j })∈E denotes that protein v_{ i } interacts with protein v_{ j }.
Given a graph G, N(v_{ i }) denotes all neighbors of v_{ i } in the PPI network. Let A be a V×V adjacency matrix, and A(i,j) denotes the confidence weight of edge (v_{ i },v_{ j }), defined as follows.
where N(v_{ i })∩N(v_{ j }) is the intersection of neighbors between N(v_{ i }) and N(v_{ j }), and N(v_{ i })∪N(v_{ j }) is the union of neighbors between N(v_{ i }) and N(v_{ j }).
Since two vertices having a larger proportion of common neighbors, one vertex can move to another vertex with great probability. A canonical flow matrix M indicates the probability of transitions via a random walk, and M(i,j) represents the probability of a transition from v_{ i } to v_{ j }, defined as follows.
where n is the number of all vertices in the graph, and each column of M sum up to 1.
Markov cluster algorithm
Markov Cluster Algorithm proposed by Stijn van Dongen [19], is an iterative process of applying two operations, namely Expand and Inflate. These two operations are alternately applied to an initial stochastic matrix M, iterating until convergence. In addition, Prune is performed at the end of each iteration, in order to remove entries with very small values.
Expand and inflate
The operation of Expand is simply expressed as M_{ exp }=M×M. We calculate M_{ exp } on the basis of M, and then assign the obtained matrix M_{ exp } to M.
The operation of Inflate raises each entry in M using parameter r, and renormalizes elements in each column that sum up to 1. Then, we assign the obtained matrix M_{ inf } to M. The operation of Inflate, named by M_{ inf }(i,j), is expressed as follows.
where n is the number of all vertices in the graph, and r is the parameter of Inflate, by default r=2,.
Prune
In the iterative process, there are some entries with very small values, and let these entries to be zero. This operation can make convergence faster, and keep the key part of aggregation information.
We use L_{ j }={kM(k,j)>0} to represent a collection of vertices in column j with values greater than zero; in other words, it is a collection of vertices that flow to vertex v_{ j }. We calculate the average value of all elements in L_{ j } as follows.
And also, we calculate the threshold to filter entries with small values in column j of M as follows.
where w is a parameter to adjust the threshold value, by default w=1.
We remove entries with very small values less than thd(j) in column j of M, filled with zero. After the operation, M must be renormalized, and elements in each column of M sum up to 1.
Cluster
After lots of iterations, we find that most vertices flow to one vertex, and there exists one nonzero entry per column in the flow matrix M. We assign all vertices flowing to the same vertex as belonging to one cluster.
Feature analysis
We propose some significant features, such as graph information and gene expression, to filter and modify complexes predicted by Markov Cluster Algorithm.
Connection
The direct connection (edge) in the PPI network, denotes that one protein interacts with another protein. We not only use the interaction information, but also consider indirect connection with a nlength shortest path as nconnection.
If there exists a nconnection between v_{ i } and v_{ j }, we can define Connect(v_{ i },v_{ j },n)=1; else, Connect(v_{ i },v_{ j },n)=0. Moreover, PathNum(v_{ i },v_{ j },n) denotes the total number of nlength shortest paths from v_{ m } to v_{ n }.
Given a protein v_{ k } and a complex C, we calculate the ratio of nconnection proteins in C from v_{ k }, defined as follows.
Also, we calculate the ratio of total nlength shortest paths for nconnection proteins in C from v_{ k }, defined as follows.
Here, we calculate these features of 2connection and 3connection.
Density
We can use the density of complex C to describe intensive degree of nconnection proteins, defined as follows.
When a protein v_{ k } is added into complex C, a new complex C^{′} can be formed. We calculate the density difference between these two complexes, as follows.
where C^{′}={C,v_{ k }}.
Here, we also calculate these features of 2connection and 3connection.
Coexpression
Gene expression data could reflect features of proteins under various conditions in a biological process [43, 51]. It is the numerical expression value of one protein within the time period. For a protein, the fluctuation range of its expression value is not the same. We normalize each value to compare the similarity of expression intervals of proteins, as follows.
where T_{ i }(l) represents the expression value of protein v_{ i } at the time point l.
On 36 intervals,Fig. 2 shows the gene expression data for eIF3 complex, and Fig. 3 shows the gene expression data for Succinate Dehydrogenase complex (complex II). We find that six proteins in one complex tend to have similar tendency of expression values at the fixed time interval (indicated as grayshadowed intervals).
Two proteins have a similar degree of expression at the same time interval leading to a high coexpression value. If the gene expression data of proteins are not similar, their coexpression value is low. Therefore, we calculate the coexpression value E_{ co }(v_{ i },v_{ j }) of proteins v_{ i } and v_{ j }, defined as follows.
where m is the number of expression intervals.
For a complex C, we can measure the coexpression value, as follows.
And, the coexpression value between one protein v_{ k } and a complex C is defined as follows.
We calculate average coexpression value of all pairs of proteins in the PPI network, defined as E_{ co }(avg). If E_{ co }(v_{ i },v_{ j })>E_{ co }(avg), we set Co(v_{ i },v_{ j })=1, else, Co(v_{ i },v_{ j })=0.
We calculate the ratio of coexpression protein pairs in a given complex C, as follows.
When a protein v_{ k } is added into complex C, a new complex C^{′} can be formed. We calculate the coexpression difference between these two complexes, as follows.
where C^{′}={C,v_{ k }}.
For protein v_{ k }, we calculate the number of coexpression proteins in a complex C, as follows.
Also, we calculate the ratio of coexpression proteins for protein v_{ k } in a complex C, as follows.
Complex detection
We set two thresholds, a lower bound and a higher bound for each of three features, to filtering predicted complexes: Den(C,n), E_{ co }(C), Cotadio(C). We reserve complexes with high qualities, discard complexes with low values, and modify median complexes. Algorithm 1 shows the overall algorithm of filtering method.
We use a linear function of seven features to determine how to modify a given complex: ConnectRatio(v_{ k },C,n), PathRatio(v_{ k },C,n), DenDiff(v_{ k },C,n), E_{ co }(v_{ k },C), CoDiff(v_{ k },C), CoProNum(v_{ k },C), CoProRatio(v_{ k },C). We delete proteins in a complex with low qualities, and add neighbor proteins with high values into the complex. Algorithm 2 shows the overall algorithm of modifying method.
Results and discussion
Experiments show that our method achieves better results than some stateoftheart methods for identifying protein complexes on PPI networks, with the prediction quality improved in terms of many evaluation criteria.
Data set
Our method is applied on two experimental yeast PPI networks. One is retrieved from the Database of Interacting Proteins (DIP) [52], which was used in COACH [34]. Another is downloaded from Munich Information Center for Protein Sequences (MIPS) database [53]. We remove selfconnecting interactions and repeated interactions. The DIP network includes 4930 yeast proteins and 17,201 interactions, and the MIPS network contains 12,319 interactions among 4546 yeast proteins.
All predicted complexes are compared with the benchmark data, referred to as CYC2008 [54]. There are 408 manually annotated complexes, which are considered as the gold standard data.
We analyze gene expression data GSE3431 [55] downloaded from Gene Expression Omnibus (GEO), entitled as logic of the yeast metabolic cycle. This data set includes 6,777 gene products that cover more than 95% proteins in PPI networks.
Assessment
At present, there are two popular measurements for evaluating the performance of complexes detection method, from many literatures [14, 56].
Sensitivity, Positive Predictive Value, Accuracy
In addition, Sensitivity (S_{ n }), Positive Predictive Value (PPV) and geometric Accuracy (Acc) have recently been proposed to evaluate the quality of protein complex prediction [56]. Give n benchmark complexes and m predicted clusters, let as T_{i,j} denote the number of common proteins between the ith benchmark complex and the jth predicted cluster. Then, S_{ n }, PPV and Acc are defined as follows.
Generally, S_{ n } indicates that predicted complexes have a good coverage of proteins in benchmark complexes, and PPV indicates that predicted complexes are likely to be true positive. The geometric accuracy (Acc) indicates the tradeoff between S_{ n } and PPV. It is obtained by computing the geometrical mean of them.
Precision, Recall, Fmeasure
The overlapping score O(C_{ p },C_{ b }) is used to assess how effectively a predicted complex C_{ p } matches a benchmark complex C_{ b } [14], defined as follows.
where C_{ p } is the number of proteins in the predicted complex, and C_{ b } is the number of proteins in the benchmark complex. If a predicted complex C_{ p } that has no common proteins with a benchmark complex C_{ b }, then O(C_{ p },C_{ b })=0.
Usually, a predicted complex and a benchmark complex are considered as a match if their overlapping score is no less than a threshold value [14]. Let P be the set of complexes predicted by computational methods and B be the set of benchmark complexes in the PPI network. Then, the number of complexes in P at least matching one real complex is denoted by N_{ cp }={C_{ p }C_{ p }∈P,∃C_{ b }∈B,O(C_{ p },C_{ b })≥ω}, while the counterpart number in B can be denoted by N_{ cb }={C_{ b }C_{ b }∈B,∃C_{ p }∈P,O(C_{ p },C_{ b })≥ω}, by default ω=0.2.
Based on above definitions of N_{ cp } and N_{ cb }, Precision and Recall can be defined as follows.
And, Fmeasure is their harmonic mean, defined as follows.
Filtering threshold
We consider three features Vector(C) to filtering predicted complexes. Based on coexpression value as Eco(C), CoRatio(C) as well as graph information as Den(C,n), the preliminary complex clustering result will be determined to be either reserved, removed or further modified. Two thresholds including a upper bond and a lower bond are set for each of the three features. The Tables 1, 2 and 3 show the extent of improvement of our result enhanced solely by each one of the three features respectively under distinctive thresholds. Both the gene expression and graph information are effective and make a contribution to a significantly improved result by 0.04 to 0.10 in Precision.
In addition, the optimized parameter thresholds are obtained from the three tables.The minimum value of E_{ co }(C) can be set to 50; that is, our method removes complexes with low coexpression values, and N_{ cb } and Recall decrease slightly, but Precision increases a lot. The maximum value of E_{ co }(C) can be set to 80; that is, our method reserves complexes with high coexpression values, and Precision and FMeasure increase slightly. Moreover, the threshold of CoRatio(C) can be set to (0.75,0.20), and the threshold of Den(C,n) can be set to (0.18,0.06).
Modifying analysis
We use a linear function of seven features to evaluate the probability of a protein adding into a complex, as follows.
We discuss the effectiveness of our linear function, by using some randomly generated positive and negative samples to regression. First, we randomly select a protein in the network, and choose the size of generated complex. Then, we randomly choose another protein from the collection of neighbors. Repeat this step until producing a complex. Finally, we calculate the neighboring collection of this generated complex. If adding a neighboring protein makes new complex better than old one, we assign it is positive; else, it is negative. Similarly, we traverse all proteins in this complex. If deleting a internal protein makes new complex better than old one, we assign it is positive; else, it is negative. We use 1894 positive samples and 9309 negative samples to produce the optimal parameters, as w={0.01,0.02,0.01,0.24,0.36,0.03,0.33}. Gene Expression information as CoProRatio(vk,C),CoDiff(vk,C), Eco(vk,C) contribute the most.
Deleting
For CYC2008, we filter some complexes with less than three proteins, keeping 236 complexes with average size of 6.68 proteins. For each complex, we randomly put in a protein from PPI network to form a new complex. When randomly delete a protein, the probability of correct deleting is \(P_{random} = \frac {1}{1 + 6.68} \approx 0.130\), but accuracy of our deleting method is 0.48. When randomly putting in two or three proteins, accuracy of our deleting method are 0.63 and 0.70, respectively. The analysis of deleting method is shown in Table 4.
Adding
On DIP network, we generate 1507 complexes and use P(v_{ k },C) for adding neighboring proteins. When randomly add a protein, the probability of correct adding is \(P_{random} = \frac {6189}{105553} \approx 0.0586\). However, accuracy of our adding method is 0.0765 if P>0.5, and accuracy of our adding method is 0.3333 if P>0.8. The analysis of adding method is shown in Table 5.
Comparison to existing methods
We compared the performance of our method with three existing methods, such as COACH, ClusterONE and MCL. COACH is a novel coreattachment method to detect complexes with two stages [34]. It detected cores of complexes and then added attachments into these cores to form biologically meaningful structures. ClusterONE is a method for detecting potentially overlapping complexes from the PPI data, clustering with overlapping neighborhood expansion [18]. MCL is a graph clustering algorithm based on stochastic flow simulation [19], which is effective in clustering biological networks. To evaluate our method, we test on two experimental yeast PPI networks.
On DIP network, results by our method and three existing methods are shown in Table 6. Our method has Precision and FMeasure values of 0.6004 and 0.5528. COACH achieves Precision and FMeasure values of 0.2896 and 0.3211, ClusterONE achieves Precision and FMeasure values of 0.4252 and 0.3675, and MCL achieves Precision and FMeasure values of 0.2353 and 0.2941. Comparing to existing methods, our method improves Precision value by at least 0.1752, and FMeasure value by at least 0.1853.
On MIPS network, results by our method and three existing methods are shown in Table 7. Our method has FMeasure value of 0.3774. COACH achieves FMeasure values of 0.2497, ClusterONE achieves FMeasure values of 0.3326, and MCL achieves FMeasure values of 0.3158. Comparing to existing methods, our method improves FMeasure value by at least 0.0448, and also improves S_{ n } value by at least 0.0771. Although our method did not achieve the best recall value, as we can see from the table, method with high recall values like DPClus and RRW, unavoidably have a particular poor precision, which indicates the high recall is based on counting into a overall large number of clusters and hence the precision is weakened. Comparatively, our method remains a relatively high recall value and achieves the best precision revealing the overall efficiency of our model.
An available COACH system is downloaded from http://www.comp.nus.edu.sg/~lixl/, and a fast and free implementationof ClusterONE is available at http://www.paccanarolab.org/clusterone/. Also, we compare our method to many other complex detection methods in Table 8, and results of these methods are from many literatures [10, 14, 30, 33].
Running time
Our experiments are conducted on a PC with Intel(R) Xeon(R) CPU E51620 of 3.7 GHz and 12.0 GB RAM. Here, we compare the running time of different methods on the PPI network with 4930 nodes and 17201 edges. Our method completes complex detection within 736 s, as shown in Table 9.
Conclusions
We propose a novel method to identify complexes on PPI networks. First, we design an edgeweighting MCL method to calculate complexes on PPI networks. Second, we propose some significant features, such as graph information and gene expression, to filter and modify complexes predicted by Markov Cluster Algorithm.
Experiments show that our method achieves better results than some stateoftheart methods for identifying complexes on PPI networks. To evaluate our method, we test on two experimental yeast PPI networks. On DIP network, our method has Precision and FMeasure values of 0.6004 and 0.5528, improves by at least 0.1752 and 0.1853. On MIPS network, our method has FMeasure value of 0.3774, improves by at least 0.0448.
Abbreviations
 CMC:

Clustering?based on maximal cliques
 CPM:

Clique percolation method
 Den:

Density
 DenDiff:

Density difference
 DIP:

Database of interacting proteins
 GEO:

Gene expression omnibus
 MC:

Monte Carlo optimizationbased technique
 MCL:

Markov cluster algorithm
 MIPS:

Munich information center for protein sequences database
 PathNum:

Path number
 PPI:

Protein protein interaction
 RNSC:

Restricted neighborhood search clustering
 SPC:

Superparamagnetic clustering
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Acknowledgements
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Funding
This research and this article’s publication costs are supported by a grant from the National Science Foundation of China (NSFC 61772362) and the Tianjin Research Program of Application Foundation and Advanced Technology (16JCQNJC00200).
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All datasets, feature sets and the relevant algorithm are available for download from https://figshare.com/s/0737e9bdaa6b9ec4c2e2.
About this supplement
This article has been published as part of BMC Systems Biology Volume 12 Supplement 4, 2018: Selected papers from the 11th International Conference on Systems Biology (ISB 2017). The full contents of the supplement are available online at https://bmcsystbiol.biomedcentral.com/articles/supplements/volume12supplement4.
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ZZ, JS and FG conceived the study. ZZ and JS performed the experiments and analyzed the data. ZZ and FG drafted the manuscript. All authors read and approved the manuscript.
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Correspondence to Fei Guo.
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Zhang, Z., Song, J., Tang, J. et al. Detecting complexes from edgeweighted PPI networks via genes expression analysis. BMC Syst Biol 12, 40 (2018) doi:10.1186/s129180180565y
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Keywords
 Complex detection
 PPI networks
 Edgeweighting scheme
 Graph information
 Gene expression analysis